Finkelshtein D. L.
Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1699-1719
We consider the convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation measures and functionals. In particular,the convolution of Gibbs measures is studied. We also describe a relationship between invariant measures with respect to some operator and properties of the corresponding image of this operator on correlation functions.
Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1547-1567
We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space) and study some of their properties. A relationship between the $\ast$-convolution and the convolution of measures on spaces of finite configurations is described. Properties of the operators of multiplication and differentiation with respect to the $\ast$-convolution are investigated. We also present conditions under which the $\ast$-convolution is positive definite with respect to the $\star$-convolution.